On the Convergence of the Summation Formulas Constructed by Using a Symbolic Operator Approach

Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue

Research output: Journal ArticleArticlepeer-review


This paper deals with the convergence of the summation of power series of the form Σ a ≤ k ≤ b f(k)x k , where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

Original languageAmerican English
JournalComputers and Mathematics with Applications
StatePublished - 2006


  • Applied Mathematics
  • Mathematics

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